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2 years ago

What is the solution to the following system of equations?

Mathematics

2 answers:

Sloan [31]2 years ago

8 0

Answer:

The answer to your question is (6, 0)

Step-by-step explanation:

Solve the system of equations by elimination

x - 4y = 6 (I)

2x + 2y = 12 (II)

Multiply (II) by 2

x - 4y = 6

4x + 4y = 24

Simplify

5x + 0 = 30

Find x

5x = 30

x = 30/ 5

x = 6

Find "y"

6 - 4y = 6

-4y = 6 - 6

-4y = 0

y = 0/-4

y = 0

erastova [34]2 years ago

5 0

Answer:

(6,0)

Step-by-step explanation:

Given equations are:

\[x - 4y = 6\] -------------------- (1)

\[2x + 2y = 12\] -------------------- (2)

Multiplying (1) by 2 :

\[2x - 8y = 12\] -------------------- (3)

Calculating (2) - (3) :

\[2x + 2y -2x + 8y = 12 - 12\]

=> \[10y =0\]

=> \[y = 0\]

Substituting the value of y in (1):

\[ x = 6 \]

So the required solution of the system of equations is x=6,y=0. This can be alternatively expressed in coordinate notation as (6,0).

You might be interested in

Divide: (-7x+x^2+15)÷(-3+x)

kakasveta [241]

Since the divisor is in the form (x + #) or (x - #), This can be done by synthetic division.
First put the polynomial ion descending order: x^2 - 7x + 15
Take the coefficients of the terms and follow these steps:

3 | 1 -7 15
   3 -12
___________ Bring down the 1, multiply the 3 by the 1 and place under the
   1 -4    3 -7, then add.
   Multiply 3 by -4, place under the 15, then add.
   The bottom row is our answer. Since the problem started with a second power, the answer will start with a first power.
The bottom row are the coefficients of the terms and the last number is the remainder.
x - 4 remainder 3 ALSO WRITTEN x - 4 + 3/(x -3)

3 0

2 years ago

Six-four million, one hundred eighty-six thousand, three hundred square miles in standard form

Zielflug [23.3K]

Answer:

64,186,300 square miles

I'm sorry if I misunderstood.

Good luck mate! :)

Please add Brainliest if you'd like, not that it matters.

Remember to try your best every day!

6 0

3 years ago

Which of the following is an equation of the line that passes through the point (−2, 3) and is perpendicular to the graph of the

Ludmilka [50]

The equation of the line is $y=-\frac{1}{3}+\frac{7}{3}$

Explanation:

The given equation is $y=3 x-2$

<u>Slope:</u>

Since, the equation of the line is perpendicular to the equation $y=3 x-2$ , then, the slope is given by

$m=-\frac{1}{3}$

Hence, the slope is $m=-\frac{1}{3}$

<u>Equation of the line:</u>

The equation of the line can be determined using the formula,

$y-y_1=m(x-x_1)$

Substituting the point (-2,3) and the slope $m=-\frac{1}{3}$ , in the above formula, we get,

$y-3=-\frac{1}{3}(x+2)$

Simplifying, we get,

$y-3=-\frac{1}{3}x-\frac{2}{3}$

$y=-\frac{1}{3}x-\frac{2}{3}+3$

$y=-\frac{1}{3}+\frac{7}{3}$

Therefore, the equation of the line is $y=-\frac{1}{3}+\frac{7}{3}$

8 0

3 years ago

Pete's monthly housing budget is $2,250. His monthly costs are $215.75 for insurance, $143.50 for utilities, and $273 for taxes.

Afina-wow [57]

Answer:

Option B. house B; monthly payment of $1,550.89 is the correct answer.

Step-by-step explanation:

In order to calculate the highest payment Pete can afford we have to subtract his expenses from his housing budget.

Given

Total housing budget = $2250

Monthly costs = $215.75

Utilities = $143.50

Taxes = $273

First all expenses can be added together to subtract from the housing budget.

$Monthly\ costs = Insurance\ +\ Utilities\ +\ taxes\\ = \$215.75 + \$143.50 + \$273\\= \$632.25$

Now the total monthly cost will be subtracted from housing budget.

$Amount\ for\ monthly\ payment = Housing\ budget - Monthly\ Expenses\\=\$2250\ -\ \$632.25\\=\$1617.75$

Hence, he saves $1617.75 for monthly payment.

Looking at the options, C and D will be ruled out as both the quantities are greater than 1617.75

Option A and B both are smaller than 1617.75 but as $1,550.89>$1,327.18, Option B is the highest monthly payment Pete can afford.

Hence,

Option B. house B; monthly payment of $1,550.89 is the correct answer.

6 0

3 years ago

What does "x" equal when <img src="https://tex.z-dn.net/?f=log%20_%7B3%7D27%20%5E%7B2x%7D%20%3D%203" id="TexFormula1" title="log

Leviafan [203]

$\log_327^{2x}=3\\
3^3=27^{2x}\\
27=27^{2x}\\
2x=1\\
x=\dfrac{1}{2}$

6 0

3 years ago